In his famous paper of 1905 Einstein postulated that the velocity of light be constant in all inertial systems. Measurements with increasing accuracy confirmed the justification of this conjecture, so that today we have in fact replaced the normal meter by the cesium second and nine numbers. A physicist measuring the velocity of light, who would come up with a result different from the nine legal numbers, would just have used an illegal system of units.
In his General Theory of Relativity (GRT) Einstein conceded that the velocity of light may depend on the gravitational potential which would explain the deflection of light passing heavy masses. In order to verify any variation of c experimentally, one would need to measure the velocity of light at different gravitational potential. This is, however, no longer possible having abolished the normal meter. It is, therefore, now custom to postulate also in GRT the constancy of c and explain the observed deflection and the longer duration of the passage of light near gravitational centers by a distorted metric of space.
There are, however, experiments carried out on earth which are much easier to interpret when we follow Einstein?s original conjecture, namely that the velocity of light depends on the gravitational potential. Curiously enough, these experiments are commonly taken as a confirmation of GRT, but this is in fact only true when we allow for a variation of the velocity of light. If not, a violation of the energy principle would be the consequence.
In this note we discuss the famous experiment by Pound and Rebka of 1960 who used the M?ssbauer effect to measure the ?apparent weight of photons?. We compare it with the ?Maryland experiment? of Alley proving that atomic clocks run faster with increasing distance from the gravitational center. Both experiments are frequently said to confirm in an ?equivalent? way a simple formula derived in GRT, but, as already hinted by Pound and Rebka, this is actually not true. We include in our comparison a simple gedanken experiment which is based on the conservation of energy and we come to the conclusion that the real experiments may be reconciled when we allow for a variation of the velocity of light.
